Let $\displaystyle p$ be a prime such that $\displaystyle p>(n^2+n+k)^2+k$. ( $\displaystyle

n,k \in \mathbb{Z}^ +

$ )

Consider the sequence: $\displaystyle

n^2 ,n^2 + 1,...,\left( {n^2 + n + k} \right)^2 + k

$.

Prove that there's a pair $\displaystyle (m,m+k)$ of integers from our sequence, such that $\displaystyle

\left( {\tfrac{m}

{p}} \right)_L = \left( {\tfrac{{m + k}}

{p}} \right)_L = 1

$

This is a lovely problem, have fun!. (Happy)

PS: By the way, I'd posted

2 problems like in January, NCA gave a solution for 1, but the other is waiting! (haha, and it is a nice problem too)